To make the béarnaise, put the shallot, peppercorns, wine and vinegar in a small saucepan. Bring to the boil and simmer until you have 1–2 tablespoons left. Drain through a sieve and discard the peppercorns.
Place the butter in a small saucepan and melt over a medium heat then remove from the heat and set aside.
Place the egg yolks into a food processor and blend with the vinegar and white wine reduction. Slowly pour in the melted butter, blending all the time. Stir in the tarragon and season with salt and pepper and keep warm.
To make the halibut, place all the ingredients except for the halibut in a medium saucepan with 50ml/2fl oz water and bring to a simmer. Gently poach the halibut for 5–6 minutes.
To make the artichokes, heat some olive oil in a large frying pan over a medium heat and fry the artichokes until golden-brown on both sides. Add the chopped shallots, hazelnuts, parsley and garlic to the pan and cook for another 5 minutes.
Fill a deep-fat fryer or a large, deep, heavy-bottomed pan two-thirds full with the oil. Heat to 180C (a cube of bread should turn brown in one minute when dropped in.) CAUTION: Hot oil can be dangerous. Do not leave unattended.
Mix the caster sugar and salt together in a bowl. Deep-fry the kale until crisp, drain on kitchen paper then season with the sugar and salt mixture.
Loosen the béarnaise slightly with 1 or 2 tablespoons of the poaching liquor and a tablespoon of cream.
To serve, divide the artichokes between two plates and top with the poached fish. Spoon over the béarnaise and glaze with a cook’s blow torch. Serve the kale crisps on the side.